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A free energy landscape of the capture of CO2 by frustrated Lewis pairs

Lei Liu,a,b*† Binit Lukose,c Bernd Ensing d*

a Department of Physics & Earth Sciences, Jacobs University Bremen, Campus Ring

1, 28759 Bremen, Germany

b Mulliken Center for Theoretical Chemistry, Institute for Physical and Theoretical

Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany

c School of Electrical and Computer Engineering, Boston University, 02215 Boston, USA

d Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, 1098 XH

Amsterdam, The Netherlands

† Current address: Max Planck Institute for Polymer Research, Ackermannweg 10, 55128

Mainz, Germany

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Abstract: Frustrated Lewis pairs (FLPs) are known for its ability to capture CO2.

Although many FLPs have been reported experimentally and several theoretical studies

have been carried out to address the reaction mechanism, the individual roles of Lewis

acids and bases of FLP in the capture of CO2 is still unclear. In this study, we employed

density functional theory (DFT) based metadynamics simulations to investigate the

complete path for the capture of CO2 by tBu3P/B(C6F5)3 pair, and to understand the role

of the Lewis acid and base. Interestingly, we have found out that the Lewis acids play

more important role than Lewis bases. Specifically, the Lewis acids are crucial for

catalytical properties and are responsible for both kinetic and thermodynamics control.

The Lewis bases, however, have less impact on the catalytic performance and are mainly

responsible for the formation of FLP systems. Based on these findings, we propose a

thumb of rule for the future synthesis of FLP-based catalyst for the utilization of CO2.

Keywords: CO2 capture; frustrated Lewis pairs; metadynamics simulations; free energy

surface

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TOC

The role of Lewis acids and bases in the capture of CO2 by frustrated Lewis pairs is

determined by density functional theory based metadynamics simulations.

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Introduction

The grown use of fossil fuels has resulted in large amount of CO2 being exhausted to the

atmosphere, which is considered as the major reason for global warming.1 On the positive

side, CO2 is an abundant and renewable carbon source, and it can be reduced to some

usable chemicals.2 To convert CO2 to chemicals, we firstly need to transfer the gas-phase

molecule into the solution or solid-state phase, say, by adsorbing or capturing it. This

process is typically accomplished via surface catalysis.3 However, this method is not

economically and environmentally friendly due to the introduction of transition metal

centers. Recently, Stephan and co-workers developed some concept molecules, called

“frustrated Lewis pairs” (FLPs), which may help solve the problem.4 In those molecules,

the Lewis acids and Lewis bases are sterically hindered by the presence of bulky organic

substituents, which prevent the neutralization reaction between the two components. As a

result, both reactivity of Lewis acid and base are remained in one FLP system, hence it

shows some interesting applications, such as H2 activation, capture of CO2 (see Scheme 1)

and reduction of CO2.5–12

After their discovery, the concept of FLPs have been expanded to many other systems

consisting of P/B or P/N compounds, and all these pairs have been found to capture CO2

in similar fashion. Their interesting properties have also attracted interests from

theoretical and computational chemists.13–18 Until now, two typical reaction mechanisms

have been reported in the literature. The first one, which is based on static density

functional theory (DFT) calculations, shows that the Lewis acids and bases work in a

cooperative way, and the capture of CO2 by FLPs follows a concerted mechanism.13 The

second one, which is based on the ab initio molecular dynamics (AI-MD) simulations,

shows that the capture of CO2 by FLPs follows a step-wise mechanism.16 However, no

studies on the individual roles of Lewis acid and base have been reported. Due to the lack

of that knowledge, a targeted experiment or a rational design of FLP-based catalyst for

capture and reduction of CO2 is not immediately expected.

In this study, we performed metadynamics simulations based on density functional

theory with dispersion corrections (DFT-D) to compute the free energy surface (FES) at a

finite temperature and to explore the lowest free energy reaction path for the capture of

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CO2 by the prototypical FLP: tBu3P/B(C6F5)3 (Scheme 1).13 By analyzing the FES, we

also aim to understand a detailed reaction path, specifically to unravel the individual roles

of Lewis acid and base in the capture of CO2.

Scheme 1. Capture of CO2 by an intermolecular FLP, tBu3P/B(C6F5)3.

Results and discussion

We first performed ab initio DFT-based MD simulations using a CO2−FLP adduct,

[tBu3PCOOB(C6F5)3]. We adopted this treatment because the structure of CO2−FLP

adduct has been confirmed by X-ray crystallography measurements while the structures

of free CO2 and FLP are unclear because of their complexity.13 Hence, in the course of

MD simulations, we firstly followed CO2 liberation process, instead of CO2 capture. On

the other hand, to cover the whole free energy surface, we performed relatively long

simulations that cover both the CO2 liberation and capture processes. (See Figure S1 for

the distances between P, B, C and O as a function of simulation time). Note that prior

DFT calculations show that the capture of CO2 by FLPs follows a concerted

mechanism.13,15 The reactants (FLP and free CO2 molecule) and the CO2−FLP adduct are

connected by only one transition state (TS). In the structure of TS, both P-C and B-O

distances are around 2.5 Å. That means, C and O start to interact with P and B nearly at

the same time. However, ab initio molecular dynamics (AIMD) simulations reveal a step-

wise mechanism.16 When CO2 molecule moves close to the FLP system, P-C bond is

formed, followed by the formation of B-O bond. After that, the final CO2-FLP adduct is

formed. However, this conclusion can be considered qualitative since a complete free

energy reaction path was missing. From our metadynamics simulations, we are able to

obtain the complete FES for the capture of CO2 by FLPs (Figure 1), which is more

rigorous than the reaction profile obtained either by the static DFT calculations or by

AIMD simulations. The FES depicted in Figure 1 shows a two-step reaction mechanism

(see path I): 1) Capture of C by Lewis base center, phosphorus (P): When CO2

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molecules move close to FLP pair, the C of CO2 attaches to P while O remains free. 2)

Capture of O by Lewis acid center, boron (B): After the capture of C, the remained O

attaches to B. As shown in Figure 1, the reaction could also proceed in the opposite way,

i.e., O first attaches to B and then C attaches to P (see path III). However, it is apparent

that all the points along this reaction path have high Gibbs free energies, and the barriers

for this path are much higher than that of path I. On the ground of static DFT calculations,

it is commonly believed that the reaction proceeds via a concerted mechanism. Both C

and O are captured by FLPs at the same time, and pass through only one TS. From

Figure 1, one could think of such a possibility, i.e., reactant and the product are directly

connected via the path II. However, like the path III, all points along this reaction path

have high Gibbs free energies, and this will lead to high energy barrier. Therefore, the

probability of these two paths (path II and III) will be very low. If the reaction proceeds

through path II or III, it would most likely fall back into the reactant or product states,

and then proceeds via path I. Justifying this, we obtained some structures in which both

the O−B and P−C bond lengths are about 2.5 Å around 15 ps and some other structures in

which the O−B bond length is about 2.5 Å while P−C length is about 4 Å around 25 ps.

these structures return to either reactant or product state after several picoseconds, instead

of taking path II or path III.

In short, the capture of CO2 by tBu3P/B(C6F5)3 pair is a step-wise process: firstly, C

attaches to P and then O to B. It is important to point out that, the previous AIMD

simulations has also reported a step-wise mechanism.16 However, the authors attribute

this to the explicit presence of solvent molecules in the simulations. Here, we show that

the step-wise mechanism is the nature of the reaction between FLP and CO2, as it

happens despite the absence of solvent molecules in our simulations. Eventually, the role

of the solvent is to stabilize the final products, which is a common viewpoint in the FLP

chemistry.19–21

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Figure 1. Two-dimensional free energy surface of the capture of CO2 by tBu3P/B(C6F5)3 pair. The

representative structures are depicted in Figure 3.

Now, to understand the individual roles of Lewis acids and bases and to systematically

design more efficient catalysts in the future, we have calculated one-dimensional (1D)

FES (shown in Figure 2) for the path I depicted in Figure 1. We note that the first step,

i.e., the capture of C by P atom, has two sub-steps: from A to B and from B to C. Point B

is an intermediate on the 1D FES along the path where P−C bond is formed. The first

sub-step, from A to B, has almost four times higher energy barrier than that of the second

sub-step, from B to C (11.4 kcal mol−1 versus 3.2 kcal). However, the second sub-step is

more energetically favored compared to the first one. The computed reaction Gibbs free

energy of the second sub-step is −5.6 kcal mol−1, while it is 9.5 kcal mol−1 for the first

sub-step. In short, the first step, capture of C by Lewis base (P atom), that is from A to C,

is an endothermic process with a computed reaction Gibbs free energy of 3.9 kcal mol−1

and has an overall energy barrier of 11.4 kcal mol−1. The second step from C to D is,

however, favored by thermodynamics and the computed reaction Gibbs free energy is

−5.8 kcal mol−1. Moreover, this step (from C to D) has a higher energy barrier compared

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to the first step (14.5 kcal mol−1 versus 11.4 kcal mol−1). According to the transition state

theory (Equation 1), the second step is approximately 180 times slower than the first step.

In short, the second step, which is the capture of O by B, is a thermodynamic and kinetic

control step for the capture of CO2 by tBu3P/B(C6F5)3 pair. In other words, Lewis acid

(the B(C6F5)3 molecule) plays a more important role than Lewis base (the tBu3P molecule)

in the capture of CO2. This finding is surprising since it is commonly believed that Lewis

acids and bases work in a cooperative way and both components are important for the

reactivity of FLPs with CO2. This is also different from what we have found for the H2

activation by FLPs, where Lewis acid is responsible for thermodynamics while the Lewis

base is responsible for the kinetics.22 Our finding suggests that more attention should be

paid to the Lewis acids part of FLPs in future studies regarding CO2 capture. By

thermodynamics, strong Lewis acids should be selected to make the overall reaction

endothermic. On the other hand, the Lewis acids should not be too strong, otherwise, the

final products will be too stable (i.e. D in Figure 2) and that will lead to non-reversible

reactions.23 This will not be suitable for the future utilization of the solution-phase CO2,

like the reduction of CO2 into useful chemicals. Kinetics of the reaction suggest that

relatively strong Lewis acids are needed to lower the energy barriers.17 Also, relatively

week Lewis bases should be selected to have less stable intermediates along the reaction

path (i.e. C in Figure 2), which would result in relatively small energy barriers for the

second step. However, the Lewis bases should not be too week, otherwise, the energy

barriers for the first step will become too high, which is also not suitable for the overall

reaction kinetics.

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Figure 2. One-dimensional free energy surface of the capture of CO2 by tBu3P/B(C6F5)3 pair. The

representative structures are depicted in Figure 3.

Geometrical parameters of the four minima and the three TSs are depicted in Figure 3.

The structures are denoted as A, B, C, D, TS1, TS2 and TS3 as marked in Figure 2. The

structure A is the starting point of the reaction. In this structure, the CO2 molecule is still

free, and no interactions have been found between the CO2 and tBu3P/B(C6F5)3 pair. For

evidence, the P−C and B−O distances are 3.9 and 4.0 Å, respectively and corresponding

Wiberg Bond Orders (WBO) are computed to be 0. The distance between two reactive

centers (P and B) are relative large, which is 4.7 Å. Note that the angle O−C−O of the

CO2 species is 167.8 º, which is slightly smaller than that in a free CO2 molecule (i.e.,

180.0 º). That is, the CO2 species is bent in structure A, although there are no chemical

bonds formed between the CO2 and FLP. This could be due to the weak interaction

between CO2 and FLP: CO2 interacts with crystal fields created by the FLP pair.24 The

next minimum on the potential energy surface is structure B. CO2 starts to enter the cave

of the FLP and interacts with the Lewis acid and base centers. Both P−C and B−O

distance become shorter, which are 3.2 and 3.4 Å, respectively. The computed WBO is

0.25 for P−C bond. indicating that the empty orbitals of C start to interact with the lone

pair electrons of P. However, there are no interactions between O and the Lewis acid

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center (B) since the computed WBO is 0. When the reaction continues, it will arrive at

structure C, in which the P−C bond is formed with a length of 2.1 Å and the

corresponding WBO is 0.90. In this structure, O is still free, and the B−O distance is

about 3.1 Å with a computed WBO of 0.0. Moreover, the angle O−C−O of the CO2

further decreases to 135.1 º. The final minimum of the FES is the CO2−FLP adduct,

which is given as D. In this structure, the CO2 species is finally bounded to the FLP with

distances of P−C and B−O being 1.9 and 1.6 Å, respectively. The O−C−O angle of the

CO2 species is again decreased to 130.4 º. The computed corresponding WBO shows

chemical bond characteristic of P−C and B−O bonds, which are 0.8 and 0.7, respectively.

In general, the geometric parameters of the TSs stay between their neighboring stationary

points. For example, TS1, which connects the structures A and B show shorter P−C

distance than A, but longer than B (3.7 Å > 2.7 Å > 2.2 Å). Similar trends have been also

found in the case of TS2. Essentially TS1 and TS2 correspond to the capture of C by P.

Therefore, the distance between B and O remains almost the same with small deviations

of 0.3 Å except for structure A. This trend also applies for TS3, which corresponds to the

capture of O by B. The distance between P and C remains nearly the same for C, TS3,

and D, with a change of only 0.2 Å while the distance between B and O gradually

decreases from 3.1 Å to 1.6 Å. Interestingly, the highest change in the O−C−O angle

happens when C is captured by P (from 172 º to 135 º); in the next step, i.e., capture of O

by B, the change is only about 5 º.

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Figure 3. Structures of stationary points for the capture of CO2 by tBu3P/B(C6F5)3 pair obtained from

metadynamics simulations with selected distances given in Å and Wiberg bond orders in parentheses.

Hydrogen atoms are omitted for clarity. Color legend: P yellow, B pink, C black and F green.

To gain deeper insight into the reaction mechanism, we have plotted the frontier

molecular orbitals (including the highest occupied molecular orbital, HOMO, and the

lowest unoccupied molecular orbital, LUMO) and performed natural orbital (NBO)

analysis for the important stationary points along the reaction path - structures A, C and

D (see Figure 4). In structure A, the HOMO is located on the Lewis base component

(the tBu3P molecule), and it has large contributions from the lone pair electrons of P. The

LUMO is located on the Lewis acid component (the B(C6F5)3 molecule), mainly

consisting of the empty orbitals of B. The frontier molecular orbitals indicate no orbital

interactions between the FLPs and the CO2 in structure A, which is consistent with the

geometric parameters depicted in Figure 3, where the distance between CO2 and two

reactive centers (P and B) are too large (ca. 4 Å). When the reaction arrives at structure C,

the plotted orbitals demonstrate that there are some orbital interactions between C and P.

For example, the HOMO of structure C shows that C accepts the lone pair electrons of P.

There are also some charges transferred from C to P (or electrons transfer from P to C).

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In structure A, the P and C are positively charged with partial charges of 0.68 e and 0.86

e, respectively. In structure C, the partial charge of P increases to 1.01 e and the partial

charge of C decreases to 0.66 e. The LUMO of structure C is almost identical to that of

structure A, which is mainly consisting of empty orbitals of B. Moreover, there is no

change on the partial charge of B. When the reaction arrives at structure D, more charge

transfer is seen from P to CO2, and subsequently to B. The partial charge on P is 1.32 e in

structure D while it is 1.01 e in structure C. The partial charge of B decreases to 0.68 e

while it is about 0.83 e when the distance between O and B are relatively large (ca. 4 Å in

the cases of structure A and C). It is interesting to point out that the charge of the whole

CO2 molecule is almost the same in the cases of structure C and D, which is about -0.6 e.

This finding indicates that the CO2 molecule acts as a “bridge” for the charge transfer

from P to B. For a comparison, H2 molecule has the same function and it intermediates

the charge transfer from Lewis base to acid during H2 activation by FLPs.23,25,26

Figure 4. Highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO)

and natural charges for selected atoms of the important structures provided in Figure 3. Color legend:

P yellow, B pink, C black, F green and H white.

Conclusions

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In this study, the capture of CO2 molecule by tBu3P/B(C6F5)3 frustrated Lewis pair is

revisited by the density functional theory (DFT) based metadynamics simulations. The

obtained lowest free energy reaction path is more eventful than explained in the literature,

which are obtained by static DFT calculations and ab initio molecular dynamics

simulations. Importantly, the separate roles of the Lewis acid and base are revealed in our

study, which have not been described in the literature. Specifically, the capture of CO2 by

tBu3P/B(C6F5)3 pair is a step-wise process: capture of C by P followed by capture of O by

B. It is commonly believed that the roles of Lewis acid and base centers are the same,

capturing CO2 in a cooperative way and having equal contributions. Thus, modifications

of either Lewis acid or base have the same effects on the reactivity between FLPs and

CO2. However, our findings derived from metadynamics simulations are in contrary to

that. Along the reaction path, the capture of O by B has a higher energy barrier than the

capture of C by P, indicating this step is a rate-determining step. The former process is

strongly exothermic while the latter is slightly endothermic. In short, the Lewis acid

component, B(C6F5)3, plays more important role than Lewis base component in the

capture of CO2 by FLPs. The Lewis acid component is responsible for both

thermodynamics and kinetic control. The overall thermodynamics is determined by the

strength of the Lewis acids and the overall reaction rate is determined by the strength of

the Lewis acids as well. As a thumb of rule, we suggest that future synthetic studies on

the FLP or FLP-based system for activation of CO2 should choose strong Lewis acids to

make the reaction possible in terms of thermodynamics. Moreover, a combination of

strong Lewis acids and week Lewis bases should be selected to make the reaction feasible

in terms of kinetics. In this vein, we believe that the presented conclusions are vital for

the rational design of FLP-based catalyst for activation of CO2.

Computational details

We performed all simulations similar to that in our earlier studies.22 In short, Density

functional theory (DFT) calculations were performed using CP2K program using mixed

Gaussian and plane wave (GPW) basis sets. We used the PBE density functional27

augmented with the Grimme D3 dispersion correction.28 To avoid spurious interactions

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due to the periodicity of the planewave basis, we used the Martyna-Tuckermann

technique29 and a rather large 20×20×20 Å unit cell. The ab initio molecular dynamics

(AIMD) simulations were done using NVT ensemble, with temperature set at 300 K by

making use of Nose–Hoover chain thermostat of length 4. The MD time step was 0.5 fs

and the simulations ran for 35 ps in total.

For the metadynamics simulations, we used three collective variables (CVs) to bias the

making and breaking of bonds between the P, B, C and O, for example: (1) the

coordination between the P and C, cn(P−C); and (2) the coordination between the B and

O, cn(B−O). Quadratic walls were used to avoid the sampling of uninteresting parts of

the configuration space. For example, the distance between P and B was limited to be less

than 4.5 Å, and the P−C and B−O distances were restricted to be at most 3.5 Å. The

Gaussian bias potentials were initially spawned every 25 time steps, with a height of 0.25

kcal mol‒1 and widths of 0.15 kcal mol‒1. After 20 ps of metadynamics simulation, the

height was reduced to 0.10 kcal mol‒1 and the deposit interval to 50 MD steps.

The relative reaction rates are estimated via equation 1.

(1)

where R= 1.987×10-3 kcal∙mol-1∙K-1. T is the temperature. ∆G≠ is the Gibbs activation

energy. kb and h are the Boltzmann and Planck constants, respectively.

Associated content

Supporting Information

The supporting information is available free of charge on the ACS publication website at

http://pubs.acs.org.

Additional information on path-metadynamics simulations and the Cartesian

coordinates of the seven structures depicted in Figure 3.

Movie of molecular dynamics simulations at 300 K.

Author information

- G

b RTk T

k eh

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Corresponding Authors

L.L, liulei3039@gmail.com; B. E, b.ensing@uva.nl

Notes

The authors declare no competing financial interest.

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